Information on Result #679559
Linear OA(4249, 4187, F4, 48) (dual of [4187, 3938, 49]-code), using construction X applied to C([0,24]) ⊂ C([0,17]) based on
- linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(4157, 4097, F4, 35) (dual of [4097, 3940, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(432, 90, F4, 12) (dual of [90, 58, 13]-code), using
- trace code [i] based on linear OA(1616, 45, F16, 12) (dual of [45, 29, 13]-code), using
- extended algebraic-geometric code AGe(F,32P) [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- trace code [i] based on linear OA(1616, 45, F16, 12) (dual of [45, 29, 13]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4250, 4188, F4, 48) (dual of [4188, 3938, 49]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4249, 2093, F4, 2, 48) (dual of [(2093, 2), 3937, 49]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4249, 1395, F4, 3, 48) (dual of [(1395, 3), 3936, 49]-NRT-code) | [i] | ||